Effective numerical viscosity in spectral multidomain penalty method-based simulations of localized turbulence

The numerical dissipation operating in a specific spectral multidomain method model developed for the simulation of incompressible high Reynolds number turbulence in doubly periodic domains is investigated. The method employs Fourier discretization in the horizontal directions and the discretization in the vertical direction is based on a Legendre collocation scheme local to each subdomain. Both spatial discretizations are characterized by either no or near-negligible artificial dissipation. In high Reynolds number simulations, which are inherently under-resolved, stability of the numerical scheme is ensured through spectral filtering in all three directions and the implementation of a penalty scheme in the vertical direction. The dissipative effects of these stabilizers are quantified in terms of the numerical viscosity, using a generalization of the method previously employed to analyze numerical codes for the simulation of homogeneous, isotropic turbulence in triply periodic domains. Data from simulations of the turbulent wake of a towed sphere are examined at two different Reynolds numbers varying by a factor of twenty. The effects of the stabilizers are found to be significant, i.e. comparable, and sometimes larger, than the effects of the physical (molecular) viscosity. Away from subdomain interfaces, the stabilizers have an expected dissipative character extending over a range of scales determined by timestep and the degree of under-resolution, i.e. Reynolds number. At the interfaces, the stabilizers tend to exhibit a strong anti-dissipative character. Such behavior is attributed to the inherently discontinuous formulation of the penalty scheme, which suppresses catastrophic Gibbs oscillations by enforcing C0C0 and C1C1 continuity only weakly at the interfaces.